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<H2>Overview</H2>
Polygon Overlay example that demonstrates the use of parallel_for.
<P>
This example is a simple implementation of polygon overlay, as described in 
<a href="http://citeseer.ist.psu.edu/cache/papers/cs/11981/ftp:zSzzSzftp.cs.vu.nlzSzpubzSzbalzSzcowichanzSzPolygonzSzreport.pdf/langendoen95parallelizing.pdf">
	<i>Parallelizing the Polygon Overlay Problem Using Orca</i>, by H.F. Langendoen</a>.
</P>
The solution was implemented in three forms:
<UL>
	<LI>The naive serial solution.
	<LI>The naive parallel solution, by splitting list of polygons from one map and intersecting 
	each sub-list against the entire list of polygons from the second map.
	<LI>A parallel solution where each map is split into submaps, with each resulting submap being
	intersected against the corresponding submap from the other map.  This solution requires some
	redundancy (some polygons are members of more than one submap).  To prevent multiple copies
	of a polygon from being placed in the solution map, if both polygons are duplicated (that is,
	if they both appear in more than one map), they are intersected but the result is not placed
	in the solution map.
</UL>
The only optimization in each solution is that the area of the generated sub-polygons are subtracted from
the original area of one of the source polygons.  When the remaining area is zero, the intersection process
is halted.
<P>
<i>A word about the speedup of the submap case.</i>  One may get superlinear speedup in this case (for instance a 
laptop with Intel&reg; Core(TM) Duo processor got a speedup of about 20 percent over serial.)  This results from two effects:
</P>
<UL>
	<LI>the number of threads used, and
	<LI>the fact that for each submap, the number of polygons is smaller than that for the other two cases.
</UL>
If there are, say, 400 polygons in each map, then on average the number of intersections calculated is 
approximately 80,000 (400 * 200, where 200 is the average number of polygons examined before stopping.)  
If the maps are split into 2 submaps, the time for each submap is about 200*100, or 20,000.  So even
comparing the two sets of submaps serially should result in a speedup somewhere around 2.  This number 
is affected by the number of redundant polygons being compared; this effect would eventually swamp the gain
from comparing smaller numbers of polygons per submap.  And remember the submaps are created by intersecting each
map with a rectangular polygon covering the submap being generated, which is additional work taking about N * O(400)
in the case above, where N is the number of submaps generated, that can be done in parallel.
<P>
Running the default release pover while varying the number of submaps from 1 to 1000, the speedup on the submap 
case for a 2-processor system looks like<br>
<img src="speedup.gif" alt="Table of speedup for the algorithm"><br>
</P>
<P>
One further optimization would be to sort one map, say <b>map1</b>, by maxY, and sort the other map (<b>map2</b>) 
by minY.  For <b>p1</b> in <b>map1</b>, start testing for intersection at the first <b>p2</b> in <b>map2</b> 
that intersected the last polygon tested in <b>map1</b>.  This would speed up the intersection process greatly, 
but the optimization would apply to all the methods, and the sort would have to be accounted for in the timing.
</P>
<P>
The source maps are generated pseudo-randomly in the manner described in the paper above.  That is, if
we need N polygons, then N "boxes" are chosen at random, then one-at-a-time the areas are expanded in
one of fours directions until the area hits an adjacent polygon.  When this process is finished, the
resulting map is inspected and any remaining unoccupied "boxes" are made into additional polygons, as
large as possible in each case.  So the actual number of polygons in each map will in general be larger
than the number of polygons requested (sometimes by 10% or more.)
</P>
<P>
One limitation of the program is that if the number of polygons in the source map is greater than the number of
"boxes" (pixels in the GUI case), the maps cannot be generated.
</P>

<H2>Files</H2>
<DL>
<DT><A HREF="polyover.cpp">polyover.cpp</A>
<DD>Source code for main program.
<DT><A HREF="polyover.h">polyover.h</A>
<DD>Global variables, classes and enums.
<DT><A HREF="pover_video.cpp">pover_video.cpp</A>
<DD>Source code for the GUI interface.
<DT><A HREF="pover_video.h">pover_video.h</A>
<DD>Defines for the GUI version.
<DT><A HREF="Makefile">Makefile</A>
<DD>Makefile for building example.
</DL>

<H2>Directories</H2>
<DL>
<DT><A HREF="msvs">msvs</A>
<DD>Contains Microsoft* Visual Studio* 2005 workspace for building and running the 
    example (Windows* systems only).<DT><A HREF="xcode">xcode</A>
<DD>Contains Xcode* IDE workspace for building and running the example (Mac OS* X 
    systems only).</DL>

<H2>To Build</H2>
General build directions can be found <A HREF="../../index.html#build">here</A>.  For the various UI options, see the <A HREF="../../common/index.html">common GUI code</A> build instructions.

<H2>Usage</H2>
Building via the above make commands, or via Visual Studio projects on Windows* systems, produces executable files
named pover.exe.  To run these executables directly, use one or more of the following commands.
<DL>
<DT><TT>pover.exe</TT>
<DD>Run this version (release or debug).
<DT><TT>pover.exe n:m</TT>
<DD>Run this version (release or debug) (m-n+1) times, with n threads to m threads inclusive.
<DT>To run a short version of this example, e.g., for use with Intel&reg; Threading Tools:
<DD>Build a <I>debug</I> version with the GUI turned off
    (e.g., <TT>make UI=con debug</TT>; see also the build directions above).
    <BR>Run it with a small dataset, e.g., <TT>pover.exe --polys 10 --size 5x5</TT>.
</DL>

<H2>Notes</H2>
<UL>
<LI>While running with the GUI display should yield reasonable performance in most cases, <I>running with no GUI
    display is strongly recommended</I> in order to demonstrate the full performance and scalability of the example.
</UL>

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